The behavior of turbulent flow adjacent to irrotational flow in different geometries

Turbulent flow adjacent to irrotational (or non-turbulent) flow leads to the mixing process along with entrainment, momentum transfer, and viscous diffusion. In this study, we conduct direct numerical simulations (DNS) of freely decaying compressible turbulence with a "hole" consisting of (irrotational) fluid at rest. We investigate the behavior of mixing and its statistics depending on different geometries of the irrotational flow, which are initially planar, cylindrical, and spherical. As turbulent flow penetrates to the non-turbulent flow, the mixing zone grows, and turbulence fills up the non-turbulent hole. We suggest how to measure turbulence characteristics and examine dissimilarities caused by different hole dimensions. Our results are compared with scaling derived by Barenblatt et al. (1987).